Quantum cryptography

Quantum cryptography could well be the first application of quantum mechanics at the single-quantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues. CONTENTS I. Introduction 145 II. A Beautiful Idea 146 A. The intuition 146 B. Classical cryptography 147 1. Asymmetrical (public-key) cryptosystems 147 2. Symmetrical (secret-key) cryptosystems 148 3. The one-time pad as ''classical teleportation'' 148 C. The BB84 protocol 149 1. Principle 149 2. No-cloning theorem 149 3. Intercept-resend strategy 150 4. Error correction, privacy amplification, and quantum secret growing 150 5. Advantage distillation 151 D. Other protocols 152 1. Two-state protocol 152 2. Six-state protocol 152 3. Einstein-Podolsky-Rosen protocol 152 4. Other variations 153 E. Quantum teleportation as a ''quantum one-time pad'' 154 F. Optical amplification, quantum nondemolition measurements, and optimal quantum cloning 154 III. Technological Challenges 155 A. Photon sources 155 1. Faint laser pulses 156 2. Photon pairs generated by parametric downconversion 156 3. Photon guns 157 B. Quantum channels 158 1. Single-mode fibers 158 2. Polarization effects in single-mode fibers 158 3. Chromatic dispersion effects in single-mode fibers 160 4. Free-space links 160 C. Single-photon detection 161 1. Photon counting at wavelengths below 1.1 ␮m 163 2. Photon counting at telecommunications wavelengths 163 D. Quantum random-number generators 164 E. Quantum repeaters 164 IV. Experimental Quantum Cryptography with Faint Laser Pulses 165 A. Quantum bit error rate 166 B. Polarization coding 167 C. Phase coding 168 1. The double Mach-Zehnder implementation 170 2. ''Plug-and-play'' systems 171